Similarity Criterion of Freezing Model Test considering Nonlinear Variation of Thermal Parameters with Temperature

Lin Pan,Xuelei Cheng,Jinhong Xia

doi:10.1155/2020/7468034

Abstract

The significant differences in specific heat and thermal conductivity of ice and water lead to the changes of specific heat and thermal conductivity of soil during the freezing process. This makes it hard for the temperature field similarity criterion based on constant thermal parameters to accurately reflect the temperature field evolution of soil mass caused by nonlinearity of thermal parameters in the process. Based on heat conduction differential equation considering nonlinear changes of thermal parameters, this paper uses similarity transformation method to derive the similarity criterion of the temperature field in the frozen soil model test and arrives at the conclusion that the prototype soil and model soil should meet when the original soil is used for the model test. At the same time, given the impact of the third boundary condition on the similarity criterion, the thermal physical similarity conditions for the model soil are derived. On this basis, ABAQUS finite element software is used to numerically simulate the linear and nonlinear prototype and model temperature fields. The third boundary condition considered the temperature evolution of the characteristic points during the freezing process is analyzed. The calculation results indicate that the nonlinear thermal conductivity similarity criterion established herein can correctly reflect the evolution process of the prototype frozen soil temperature field. It is also suggested that the model soil thermal parameters are reasonably calculated. At the same time, it shows that the nonlinear freezing similarity criterion of the soil, when the third boundary condition is satisfied, has clear physical meaning and higher practical value. The research results provide a practical and reasonable parameter calculation method for the model soil preparation in the frozen soil model test and a theoretical basis and technical support for the design and implementation of the water-heat-force coupling model test on frozen soil.

Highlights

Model test is a science in which, on the basis of a certain geometric-physical relationship, a model is made and tested in place of a prototype so as to have results which can be used to predict the development of the prototype according to the corresponding similarity criterion [1,2,3]
Existing literature indicates that prediction accuracy is higher when frozen soil temperature field considers thermal parameter variation with temperature [28,29,30,31]. at is, similarity criterion derived by nonlinear theory has higher prediction accuracy
By multiplying Model 2 by the time shrink ratio Ct, it can be found that the corresponding time has equal temperature value, and the temperature shrink ratio between Model 1 and Model 2 is 1. is suggests that when theoretical similarity criterion and original soil are used for model test, the similarity relationship between the prototype and the model is established

Summary

Introduction

Model test is a science in which, on the basis of a certain geometric-physical relationship, a model is made and tested in place of a prototype so as to have results which can be used to predict the development of the prototype according to the corresponding similarity criterion [1,2,3]. E existing similarity criterion for the temperature field model test of frozen soil is established based on constant thermal parameters, that is, the nonlinear changes of thermal parameters such as thermal conductivity coefficient and specific heat with temperature are not considered. At the same time, considering the impact of the third boundary condition on similarity criterion of the temperature field model test, the paper derives the conditions that the model soil should meet after material transformation in terms of thermal physical property parameters. Based on the deduced similarity criterion and the thermal property parameters of similar materials, the paper simulates numerically the linear and nonlinear frozen soil temperature fields and the third boundary condition by means of ABAQUS finite element software and analyzes temperature evolution of characteristic points

Nonlinear Heat Conduction Model and Similarity Criterion

Similarity Condition Analysis

Verification of Similarity Criterion and Model Soil Similarity Condition

Results

Conclusions